In a triangle ABC, a line XY is drawn parallel to BC meeting AB in X and AC in Y

Question

In a triangle ABC, a line XY is drawn parallel to BC meeting AB in X and AC in Y. The area of the triangle AXY is half of the area of the triangle ABC. XY divides AB in the ratio of :

Options:

A . $$1:\sqrt 2 $$

B . $$\sqrt 2 :\left( {\sqrt 2 - 1} \right)$$

C . $$1:\left( {\sqrt 2 - 1} \right)$$

D . $$\sqrt 2 :\sqrt 3 $$

Answer: Option C

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